Abstract
Infinitesimal bendings of order are considered, including analytic bendings (), of an -dimensional surface in an -dimensional () space of constant curvature. It is proved that to any solution of an times formally varied system of Gauss-Codazzi-Ricci equations there corresponds an infinitesimal bending of order of the surface in . A general form is established for solutions of this system that determine infinitesimal motions of various orders. By using these results we obtain criteria for rigidity and nonrigidity of order , and also for analytic bendability and nonbendability of a class of multidimensional surfaces of codimension in flat spaces, which contains, in particular, Riemannian products of hypersurfaces.Bibliography. 13 titles.
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